{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "205909dd",
   "metadata": {},
   "source": [
    "#  第五讲 无标度网络【实践】三"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50a95fd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#!/usr/bin/python3\n",
    "# -*- coding: utf-8 -*-\n",
    "# Author ： 单哥的科研日常\n",
    "# 关注B站和公众号：单哥的科研日常，获取更多讲解教程"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c4952b3",
   "metadata": {},
   "source": [
    "### 实验环境：\n",
    "### Python版本==3.9.6, networkx==2.6.3, matplotlib==3.5.2, numpy==1.23.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baadd879",
   "metadata": {},
   "source": [
    "## 1、精确地绘制幂律分布（见书籍进阶阅读3.B）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1752884b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入库\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import powerlaw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ea910e0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# internet网络\n",
    "edges = [tuple(line) for line in np.loadtxt(\"internet.txt\")]\n",
    "G1 = nx.Graph()\n",
    "G1.add_edges_from(edges)\n",
    "\n",
    "degree_seq1 = [G1.degree(i) for i in G1.nodes()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cc71aa28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对数坐标，线性分箱\n",
    "powerlaw.plot_pdf(degree_seq1, linear_bins = True, color = 'r', marker='o')\n",
    "# 对数坐标，对数分箱\n",
    "powerlaw.plot_pdf(degree_seq1, linear_bins = False, color = 'b', marker='s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "bb7418dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对数坐标，累积度分布\n",
    "powerlaw.plot_ccdf(degree_seq1, color = 'b', marker='o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "a02469a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# BA无标度网络\n",
    "G2 = nx.barabasi_albert_graph(100000,2)\n",
    "degree_seq2 = [G2.degree(i) for i in G2.nodes()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "83e801a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对数坐标，线性分箱\n",
    "powerlaw.plot_pdf(degree_seq2, linear_bins = True, color = 'r', marker='o')\n",
    "# 对数坐标，对数分箱\n",
    "powerlaw.plot_pdf(degree_seq2, linear_bins = False, color = 'b', marker='s')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "13287dbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对数坐标，累积度分布\n",
    "powerlaw.plot_ccdf(degree_seq2, color = 'b', marker='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de8cb0a6-e8fb-4d6a-8c00-ef3dd143eb30",
   "metadata": {},
   "source": [
    "## 2、估计度指数（见书籍进阶阅读3.C）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9b89bafa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating best minimal value for power law fit\n",
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      "kmin: 75.0\n",
      "gamma: 3.4653996272606102\n",
      "D: 0.019052157470934694\n"
     ]
    }
   ],
   "source": [
    "fit = powerlaw.Fit(degree_seq1)\n",
    "kmin = fit.power_law.xmin\n",
    "print(\"kmin:\", kmin)\n",
    "print(\"gamma:\", fit.power_law.alpha)\n",
    "print(\"D:\", fit.power_law.D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b50e4f74",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calculating best minimal value for power law fit\n",
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      "kmin: 20.0\n",
      "gamma: 3.0260001267394756\n",
      "D: 0.018545067974010565\n"
     ]
    }
   ],
   "source": [
    "fit = powerlaw.Fit(degree_seq2)\n",
    "kmin = fit.power_law.xmin\n",
    "print(\"kmin:\", kmin)\n",
    "print(\"gamma:\", fit.power_law.alpha)\n",
    "print(\"D:\", fit.power_law.D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d7d7b4e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kmin: 1.0\n",
      "gamma: 1.8920680135859635\n",
      "D: 0.46115883089539333\n"
     ]
    }
   ],
   "source": [
    "fit = powerlaw.Fit(degree_seq2, xmin = 1.0)\n",
    "kmin = fit.power_law.xmin\n",
    "print(\"kmin:\", kmin)\n",
    "print(\"gamma:\", fit.power_law.alpha)\n",
    "print(\"D:\", fit.power_law.D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "13910dc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "D_list = []\n",
    "for x in np.linspace(1,51,26):\n",
    "    fit = powerlaw.Fit(degree_seq2, xmin = x)\n",
    "    D_list.append(fit.power_law.D)\n",
    "\n",
    "plt.plot(np.linspace(1,51,26), D_list, \"ro\")\n",
    "plt.xlabel(\"$K_{min}$\")\n",
    "plt.ylabel(\"$D$\")\n",
    "plt.yscale(\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f31ab6fc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
